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Phase portraits of the quadratic polynomial Liénard differential systems

Part of: Local and nonlocal bifurcation theory Smooth dynamical systems: general theory

Published online by Cambridge University Press:  04 March 2020

Márcio R. A. Gouveia ,
Jaume Llibre  and
Luci Any Roberto
Márcio R. A. Gouveia
Affiliation:
Departamento de Matemática, Ibilce–UNESP, 15054-000 São José do Rio Preto, Brasil (mra.gouveia@unesp.br)
Jaume Llibre
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain (jllibre@mat.uab.cat)
Luci Any Roberto
Affiliation:
Departamento de Matemática, Ibilce–UNESP, 15054-000 São José do Rio Preto, Brasil (luci.roberto@unesp.br)
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Abstract

We classify the global phase portraits in the Poincaré disc of the quadratic polynomial Liénard differential systems

\dot{x}=y, \quad \dot{y}=(ax+b)y+cx^2+dx+e,
where (x, y) ∈ ℝ2 are the variables and a,b,c,d,e are real parameters.

Keywords

Quadratic systemLiénard systemPoincaré compactificationGlobal phase portraits

MSC classification

Primary: 37C29: Homoclinic and heteroclinic orbits
Secondary: 37G15: Bifurcations of limit cycles and periodic orbits
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 1 , February 2021 , pp. 202 - 216
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Copyright
Copyright © The Author(s), 2020. Published by The Royal Society of Edinburgh

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